Nuprl Lemma : decidable__l_disjoint
∀[A:Type]. ((∀x,y:A. Dec(x = y ∈ A)) ⇒ (∀L1,L2:A List. Dec(l_disjoint(A;L1;L2))))
Proof
Definitions occuring in Statement :
l_disjoint: l_disjoint(T;l1;l2),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a
Lemmas referenced :
list_induction,
all_wf,
list_wf,
decidable_wf,
l_disjoint_wf,
equal_wf,
l_disjoint_nil,
not_wf,
nil_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
append_wf,
cons_wf,
and_wf,
l_member_wf,
decidable__and2,
decidable__not,
decidable__l_member,
decidable_functionality,
iff_weakening_uiff,
l_disjoint_append2,
l_disjoint_singleton2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
rename,
because_Cache,
dependent_functionElimination,
universeEquality,
inlFormation,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairFormation,
independent_isectElimination
Latex:
\mforall{}[A:Type]. ((\mforall{}x,y:A. Dec(x = y)) {}\mRightarrow{} (\mforall{}L1,L2:A List. Dec(l\_disjoint(A;L1;L2))))
Date html generated:
2016_05_14-PM-02_22_19
Last ObjectModification:
2015_12_26-PM-04_27_09
Theory : list_1
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